## Galaxy Bias is an Isocurvature mode

This is a post I started writing nearly a year ago and have only finally got around to publishing. Part of the reason for this are my doubts about whether I should simply hold back and write it up as a standard paper or not. Since I have not done that yet, I figure it is better to talk about it here and get the ball rolling.

One of the delightful things that often happens in physics is when two things that occupy disparate parts of your brain suddenly turn out to be intimately related (e.g. the Langlands program in mathematics). There are also many lovely examples in physics but one I worked on myself was the unexpected link between parametric resonance in preheating after inflation (see e.g. here or here*) and the band structure of metals. Turns out they are deeply connected because the time-dependent Klein-Gordon equation in Fourier space is mathematically equivalent to the time-independent 1-D Schrodinger equation with the interchange of time and space. The conduction bands of metals turn out to have eigenvalues that are dual to the wavelengths at which there is no resonant particle production during preheating. This means there is even a cosmological version of Anderson localisation and other exotica (see here and here) which I think is pretty cool.

Anyway, there is another  example that I think is very interesting and which I have not seen discussed anywhere in the literature (though I may be wrong of course), other than a rather badly written conference proceedings that I put together during the first year of my PhD, available here (which may even be wrong in places, I confess I haven’t checked since reading ones early work is like going to the dentist). Since this still makes me smile I thought I would write a bit about it on the off chance that it may turn out to be a useful in some way.

To put the idea crudely: galaxy bias is intimately linked to isocurvature purturbations.

We usually define the bias between two fields (i,j) to be the (in general spacetime-dependent) factor $b_{ij}$, that relates their dimensionless density fluctuations: $\delta_i = b_{ij}\delta_j$. Typically by the word “bias” we mean the bias factor between the baryon and dark matter fields, or perhaps between the number density of galaxies and the dark matter distribution.

So, to make the link more precise, note that a space and time-independent bias of unity, $b_{ij} = 1$  for two pressureless fluids, is precisely what relativistic cosmologists would normally call an adiabatic perturbation: the two fields go up and down in exactly the same way at each point in space and time.

If there is a relative isocurvature (also known as an entropy mode for added confusion) perturbation between two fields, then the following quantity does not vanish:

$S_{ij} = \frac{\delta_i}{1+w_i} - \frac{\delta_j}{1+w_j}$

or its gauge-invariant generalisation (see e.g. the KS classic). Here $w_i = p_i/\rho_i$ as usual.

Hence we see that if $S_{ij} = 0$ we have a constant bias factor of $b_{ij} = \frac{1+w_i}{1+w_j}$. An immediate corollary of this is that if the bias is time or scale dependent, then it corresponds to a relative isocurvature perturbation for which a precise and very detailed theory in many different contexts exists (see e.g. here).  I think it is pretty cool that these widely used concepts in two very different sub-communities are actually the same thing.

Why is this link not commonly discussed? I think that partly the reason is that galaxy bias is something  observers tend to think about while isocurvature perturbations are primarily something theoretical cosmologists think about. There are deeper reasons too I expect. Galaxies are highly nonlinear objects which we then use as tracers of the underlying linear dark matter density field, so the link to standard linear cosmological perturbation theory is not clear, at least to me. Also, we are typically interested in the bias on intermediate and small scales, where linear perturbation theory has broken down.

Nevertheless, we can immediately see that when isocurvature modes decay (as happens in the standard LCDM model) we asymptotically find that the bias goes to $b=1$ any time the two fluids have the same equation of state (e.g. for baryons and CDM) and hence will become scale-independent too, a standard result. In the more general cases however, the bias between the two fluids will approach (1+w_i)/(1+w_j). However, note that on small scales the bias cannot be scale-independent even in linear theory since one cannot have exactly adiabatic fluctuations (since adiabatic modes source isocurvature modes on small scales).

Interestingly, in the case that the bias is scale-independent but is not unity, there is still an isocurvature perturbation in general, it is just highly correlated with the adiabatic mode since they are simply proportional to each other ($S_{ij} \propto \delta_i$). In the case where the bias is scale-dependent the correlation between the adiabatic and isocurvature modes degrades. It may be possible to use this in future, e.g. with the SKA and  LSST to good effect by following the HI and dark matter separately.

What is interesting about this approach is the hope that one could use some of the machinery from multi-fluid perturbation theory at first and second order to make theoretical predictions for bias, especially in the case of new scenarios (e.g. dark energy – dark matter bias).  This might be particularly useful for understanding the effects of bias on Baryon Acoustic Oscillation measurements which should be pretty linear on 100 Mpc scales.

Of course we mostly want to know about galaxy bias on nonlinear scales. Even here there is some hope. There is a very elegant formulation of “perturbation theory” in Relativity which is fully nonlinear (the covariant approach by Ellis and Bruni) and which has been worked out for multi-component fluids in this extensive review (section 2.4)**. This may allow for a fully nonlinear formulation of bias.

Is this link between bias and isocurvature modes useful otherwise? Well I had one insight that came from this way of thinking. I was considering the multi-tracer approach to reducing cosmic variance and trying to understand how it works. I realised that it works only when the different tracers are perfectly correlated with the dark matter, so that knowledge of the clustering of one gives knowledge of the clustering of the other. In this case we have three fields: the dark matter (D), and two tracers $\delta_D, \delta_1, \delta_2$. Then the three isocurvature modes $S_{ij}$ all satisfy $\big < \delta_D S_{ij} \big > \propto \big < \delta_D^2 \big >$.

I believe this method of removing the cosmic variance error will fail as soon as there is a general isocurvature mode between the two tracers or between  the tracers and the dark matter, since then one cannot use knowledge of one to predict the other and hence cosmic variance could affect the tracers differently to each other and/or from the dark matter. Of course, how would we know if this true? How plausible such isocurvature modes are is difficult to access, but it would be interesting to find out. I would certainly want it checked out before I believed a claim of detection of primordial non-Gaussianity using this method. Perhaps this is a good project to raise at the upcoming SuperJEDI workshop…

* Not at all a representative list of references!

** UPDATED : 21/5/13 Thanks to Roy for this update which I wasn’t aware of.

## The Famelab Experience

Gazing out at the crowd of 960 people, mostly teenagers, the thought occurred to me that standing alone on a big stage, attempting to entertain such a large crowd of people with science might not be everyone’s cup of tea. But when I lifted up my model of an exoplanet orbiting a star and an “ooh” washed over the crowd, that’s when I realised what Famelab is all about and why, as scientists, we should care about science communication at all.

Famelab has been called pop idols for scientists. The format is you (as a scientist or engineer) get given exactly three minutes to give a scientific talk to the public. No powerpoint allowed, only props that you can carry on stage with you. Judges are present to judge the competitors on clarity, content and charisma. But I think I only really understood Famelab when I was well into the competition. You see, this is not a scientific talk: it’s actually a scientific performance. And it’s unlike any lecture, seminar or documentary you’ve ever seen.

A plate is glued to one side of a board, on the other side are the broken pieces of an identical plate. This was to illustrate how statistics can teach you about initial conditions (like the composition of the plate for example) as an analogy to how the statistics of galaxies teach us about the early Universe.

I entered the Cape Town regionals, after some encouragement and motivation from my supervisor, where I competed against 17 other participants. The standard of the talks, with a few exceptions, was quite high. I gave a talk about statistics and its application to cosmology, using a fun prop involving a broken plate, which got me through the first round.

I then moved on, along with 8 other people to the second round of the heats. I gave a talk explaining the complex topic of how supernova observations lead to the discovery of the accelerated expansion of the Universe and what we now call dark energy. The only props I used were a light bulb, to explain the concept of a standard candle, and a tennis ball, to demonstrate how gravity normally works to explain why dark energy is so weird.

Of the 9 participants in the final round of the heats, three of us went through to take part in the finals in Grahamstown, which were held during Scifest, South Africa’s largest science festival. While there, we joined the six remaining finalists from the Johannesburg and Durban regionals. We attended a two day master class, run by Malcolm Love, a public communication skills coach and the official Famelab trainer. The master class really brought home to me the unique nature of Famelab. I doubt many scientists have spent two days doing acting, body language and storytelling exercises as part of their careers, and yet we expect scientists to naturally have these skills when they communicate to the public.

We also spent some time learning how to deal with media interviews. Scientists, especially those involved in high profile projects or receiving major awards, often find themselves thrust into the limelight without much training as to how to deal with it. Perhaps the best advice we got is prepare your message beforehand and remember the media is a great opportunity to communicate the passion we have as scientists to the public, but the media isn’t really interested in you unless you can make what you say entertaining and interesting.

It was during the master class that I realised quite why Famelab was different from all the talks I’d given in the past, both to the public and my scientific colleagues. It mostly comes from the three minute time limit. You simply can’t talk “off the cuff” and hope to have great content without going over time. In every other talk I’ve ever given, I would know the points I was going to talk about and just talk. For Famelab, I scripted each talk and delivered them word for word.

This concerned me greatly because how can you sound authentic and conversational when you’ve memorised a script? Malcolm’s expert advice was “all the best performers never make stuff up”. Even comedians, when they sound like they’ve just come up with a funny comment, they’ve probably worked on it for months. His advise when you have to write a talk, actually talk it out first. Find bits that sound good out loud and write them down. Keep talking it out until you’re happy with the content. That way, your memorised content will still sound authentic. I think it was the preparation I put into my final talk, more than anything else, which gave me the edge over my competition.

The final took place in front of an electric crowd of 960. They clapped, cheered, whistled and even gave a standing ovation for one participant who (with great zeal) spoke about saving the rhino. There were talks about the chemistry of the human body, how drugs target viruses, how plants defend themselves against bacteria, neural networks… I decided to talk about exoplanets.

I spent around two weeks working on the talk beforehand and, although I changed the delivery a great deal, the content did not change much from the master class. My fiancée, who has been an incredible support, helped me build the prop for this talk. I wanted to demonstrate how we detect exoplanets when we can’t see them. So we found a round, plastic lamp shade to serve as a star and a tennis ball (which we painted) to be our planet. The star and planet were connected by a stick and we used nylon fish gut, which is invisible on stage, to hang the mobile from (from the centre of mass) so that the planet could orbit the star. Because we wanted a real star, we put in 8 super bright LEDs with a switch to make it shine. Because the centre of mass was outside the star, you could see it wobble as the planet orbited. It also nicely demonstrated the eclipsing of the star, the other most popular method of exoplanet detection.

I didn’t realise how effective the prop would be until I got up on that stage. Because I was holding it at my side initially, there was a sense of anticipation as no-one knew what I would do with it. The moment I let it drop and start orbiting, a “ooh” whispered through the crowd. Those are the moments that make science communication worth it. When people get it, and become as excited about science as you are.

And I think that’s what Famelab is about. I feel like science communication should be a necessity, not just something we do if we have to. Not least because it’s the general public who pay for us to do science, but also because science makes people think. And with all the world’s problems, we could do with more critically thinking people. I hope that scientists see Famelab and think “hey! I could do that kind of thing!”. With just a little time and creativity, you can explain really complex concepts in a way that’s understandable and interesting. All it takes is to put yourself in the shoes of the audience and think “Is what I’m saying interesting and does it make sense?” I also feel like we should try communicating not just the cool, big concepts in our fields to the public but also our own work. Now I know I struggle to explain what I do to other cosmologists, never mind the general public but I feel like I should try because after all, if we don’t tell the rest of the world about our science, what’s the point?

So in June, I’ll be representing South Africa at the Famelab Final at the Cheltenham Science Festival. I’ll do my best to show the world just what South African scientists have to offer.

## FameLab and Radio script successes for Michelle

Congratulations to Michelle Knights who has won both the South African leg of the FameLab competition and first prize in the broadcast category of the Young Science Communicators Competition for her radio script called “The Great Debate”, a dramatised version of the real “great debate” which took place between Shapley and Curtis in 1920. Michelle will help produce her script for a local radio station while on the FameLab side, she became the 1st South African to qualify for the international finals and now travels to London in June to compete with all the national winners from the other 23 countries for two further rounds of competition. The videos of past international winners can be found at  http://www.famelab.org/.

FameLab, dubbed ‘Pop Idols for Scientists‘, gives scientists three minutes to explain a scientific topic in the most engaging way to the general public with no slides. Michelle won the local competition by talking about Bayesian statistics, supernovae and dark energy, before moving on to the gala event at Rhodes – her alma mater – where her winning talk was about the myriad of new exo-planets discovered in the last decade  - see the photos above!

Good luck Michelle! You can read about the experience from her personal point of view here.

Posted in Events, Group Members, Science | 1 Comment

## Type 1a SNe and Cosmic Dust – Joel Johansson

Just before the Christmas break we fortunate enough to have Joel Johansson form Stockholm University tell us about his research on Type 1a SNe and cosmic dust.

Joel began his talk by giving us an overview of supernovae (SNe) and their role in cosmology as standardizable candles. After showing us the very impressive existing results, Joel pointed out that we have reached a stage where systematic and statistical errors are of comparable size. As a result we must make progress in understanding both in order to improve our measurement of cosmological parameters.

One particularly important systematic is cosmic dust. Joel explained the effects of dust (both reddens and lessens the light from supernovae) and its nature. He then moved on to explain the ways in which intergalactic dust can be constrain: from quasar colour and  from x-ray halo scatter. Joel’s work involved considering both of these constraints simultaneously.

In the second half of his talk Joel discussed various aspects of the physics of dust in more detail and summarized the results of his work.

## D-Branes and The Disformal Dark Sector – Danielle Wills and Tomi Koivisto

Two weeks ago at AIMS we were visited by Danielle Wills from the University of Durham and Tomi Koivisto from the Institute for Theoretical Astrophysics in Oslo. After powering through 110km of the Cape Argus, they came in on Monday to give us a two part talk on disformal gravity and D-branes.

Tomi kicked off the proceedings with a short outline of the phenomenology of disformal gravity. He started by explaining that the basic idea was to have the gravitational and matter sectors have different metrics. Tomi explained that there exist theoretical constraints on the relationship between the two metrics — they must be related by some linear combination of a conformal and disformal transformation. The latter is a transformation where the metrics are related by a scalar function of a scalar multiplied by the product of two spacetime first derivatives of said scalar field.

After showing us that existing modified gravity models could be put into the form of particular disformal theories, Tomi explained how disformal gravity models can have screening. This is needed to ensure there can be large scale cosmological effects of the modified gravity theory without violating solar system constraints etc.

Then, after summarizing some possible tests of disformal theories, Tomi handed over to Danielle to explain the string theory motivation for such models.

Danielle began with a quick overview of string theory and its motivation. She then moved on to explain to us how disformal theories can arise generically in a large class of string compactifications.

After leading leading slowly through an outline of the mathematics, Danielle summarized the state of the work to date and the possibilities for going further.

## Cosmo-not: A Brief Look at Methods of Analysis in fMRI and in Diffusion Tensor Imaging – Paul Taylor

Far too much time has passed without updates on recent AIMS Cosmology seminars. There’s a lot to catch up on, over the last few months we’ve had talks on subjects as diverse  as functional MRI to oscillons in the early universe to disformal gravity and more.

Let me begin with a wonderful seminar Paul Taylor (a postdoc at AIMS) gave us last November on bio-medical imaging.

After outlining his talk for us and drawing some parallels to cosmology, Paul began by giving us an overview of magnetic resonance imaging (MRI). He then moved on to explain the fMRI (functional-MRI) is a subset of MRI concerned with understanding how different parts of the brain are used during the performance of various tasks.

Paul outlined an example of a typical fMRI experiment, where MRI is used to look for an increase in blood oxygenation in parts of the brain while the subject performs a repetitive task such as finger tapping. The time dependence of the brain activity is then compared with the stimulus in order to look for correlations.

After explaining how these studies can segment the brain into different regions responsible for different functions, Paul went on to explain how in more detailed studies one can look for “causal” relations in brain activity.

After detailing various methods such as PCA (principal component analysis and ICA (independent component analysis), Paul finished by summarizing once more the techniques and ideas of MRI analysis. Check out the slides below for more information.